= Laplace =

Solves the [http://en.wikipedia.org/wiki/Laplace_equation Laplace equation] `u_xx + u_yy = 0` in a rectangular domain, by iteratively applying a stencil function. 

The first argument is the number of iterations to use. The second is a BMP file containing boundary conditions.

{{{
 repa-laplace 10000 pls-400x400.bmp pls-400x400-out.bmp
}}}

== Code ==

The main algorithm is at http://code.haskell.org/repa/repa-stable/repa-examples/Laplace/src/Solver.hs

The wrapper is at http://code.haskell.org/repa/repa-stable/repa-examples/Laplace/src/Main.hs

== Test Data ==

In the input file, greyscale gives the boundary conditions, blue specifies where to determine the solution. 

|| pls-400x400.bmp || pls-400x400-out.bmp ||
|| [[Image(Examples/Laplace:pls-400x400-thumb.png)]] || [[Image(Examples/Laplace:pls-400x400-out-thumb.jpg)]] ||
|| [http://code.haskell.org/repa/wiki/images/pls-400x400.bmp full size] || [http://code.haskell.org/repa/wiki/images/pls-400x400-out.bmp full size] ||

== Runtime == 

Compiled with GHC 6.13.20100309. 400x400 image. 1000 iterations.

Running on a Intel i7 iMac. 2.8Ghz, 4 cores x 2 threads/core. 256k L1, 8MB L2, 8GB main memory.

Times stated include IO.

|| Threads || Time(s) || 
|| 1  || 64.67 ||
|| 2 || 37.29 || 
|| 3 || 27.45 || 
|| 4 || 31.96 || 
|| 5 || 28.08 ||
|| 6 || 24.39 ||
|| 7 || 23.83 || 
|| 8 || 24.67 ||